In mathematics, especially functional analysis, a normal operator on a complex Hilbert space is a continuous linear operator
that commutes with its hermitian adjoint N*:
Normal operators are important because the spectral theorem holds for them. Today, the class of normal operators is well-understood. Examples of normal operators are
- unitary operators:
- Hermitian operators (i.e., selfadjoint operators): ; (also, anti-selfadjoint operators: )
- positive operators:
- normal matrices can be seen as normal operators if one takes the Hilbert space to be .
Read more about Normal Operator: Properties, Properties in Finite-dimensional Case, Normal Elements, Unbounded Normal Operators, Generalization
Famous quotes containing the word normal:
“The normal present connects the past and the future through limitation. Contiguity results, crystallization by means of solidification. There also exists, however, a spiritual present that identifies past and future through dissolution, and this mixture is the element, the atmosphere of the poet.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)